std:numeric_limits<double>::epsilon definition

numeric_limits::espilon returns the difference between 1 and the next double. So, should I understand that the distance between two adjacent doubles is not always the same, for instance between 2 and the next double?

And if yes could I have a piece of explanation 开发者_如何学C?

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The "density" of floating-point numbers decreases a lot as you get farther away from zero.

This is because IEEE floating-point is stored essentially as scientific notation, so range is favored over uniform precision. (If it was uniform precision, it would be fixed-point, not floating-point.)

In other words, numbers are stored in the form Significand * 2^exponent, so if the exponent gets large, a small change in the significand produces a large change in the number (and vice-versa).

So no, you can't assume that the difference between 2 and the next double is the same as epsilon; it isn't.

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Doubles are floating point numbers. They consist of a signum, a significand and an exponent.

The higher the exponent, the larger the difference between a double and its successor.

The lower the exponent, the smaller the difference between a double and its successor.